Researchers collect large amounts of user interaction data with the goal of mapping user's workflows and behaviors to their high-level motivations, intuitions, and goals. Although the visual analytics community has proposed numerous taxonomies to facilitate this mapping process, no formal methods exist for systematically applying these existing theories to user interaction logs. This paper seeks to bridge the gap between visualization task taxonomies and interaction log data by making the taxonomies more actionable for interaction log analysis. To achieve this, we leverage structural parallels between how people express themselves through interactions and language by reformulating existing theories as regular grammars. We represent interactions as terminals within a regular grammar, similar to the role of individual words in a language, and patterns of interactions or non-terminals as regular expressions over these terminals to capture common language patterns. To demonstrate our approach, we generate regular grammars for seven existing visualization taxonomies and develop code to apply them to three public interaction log datasets. In analyzing these regular grammars, we find that the taxonomies at the low-level (i.e., terminals) show mixed results in expressing multiple interaction log datasets, and taxonomies at the high-level (i.e., regular expressions) have limited expressiveness, due to primarily two challenges: inconsistencies in interaction log dataset granularity and structure, and under-expressiveness of certain terminals. Based on our findings, we suggest new research directions for the visualization community to augment existing taxonomies, develop new ones, and build better interaction log recording processes to facilitate the data-driven development of user behavior taxonomies.
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